Image Registration Errors Research Articles

WE‐E‐BRC‐07: Evaluate Reproducibility of 4DCT Registration‐Based Lung Ventilation Measurement with Gamma Comparison Method

Purpose: The regional lung pulmonary function can be calculated by computing the Jacobian of image registration deformation field. Radiation‐induced pulmonary function changes are assessed by comparing pulmonary function before and after radiation therapy (RT). Due to the probably different breath pattern and effort, uncertainties from 4DCT imaging and registration error, we need to first establish the measurement reproducibility. We also introduce gamma comparison method to compensate space disalignment in two distributions. Methods: Two repeated 4DCT data sets scanned with 30 minutes interval before RT from two patients are used in this study. Tissue volume preserving nonrigid registration algorithm with Laplacian regularization constraints was applied to register the maximum exhalation image to the maximum inhalation image for the calculation of local lung expansion as a measurement of regional pulmonary function in two scans. We compared the two pulmonary functions and analyzed the pulmonary function ratio map. Gamma comparison method is introduced to tolerate possible error in image acquisition and image registration. Mean and standard deviation of pulmonary function ratio map and gamma pass percent are calculated to measure reproducibility. Results: The registration accuracy analysis indicated our registration error is on the order of 1.0 mm. Most lung tissue has a reproducible pulmonary function. Reproducibility near the diaphragm is worse than other regions. The standard deviation of function ratio map is respectively 0.0352 and 0.0495. The gamma comparison pass percent is respectively 84% and 87%. Further plots suggest most of the lung function is reproducible in 2 scans. Conclusions: We analyzed the reproducibility to measure regional pulmonary function using 4DCT and image registration. We compared the regional lung function in two repeated 4DCT scan and discussed the function ratio map. We also introduced a gamma comparison method to quantify reproducibility.This work was supported in part by NIH grant HL079406 and EB004126.

Registration of CT to 3D ultrasound using near-field fiducial localization: A feasibility study

Objective: Registration of ultrasound to computed tomography (CT) images is used in several image-guided procedures, including laparoscopic surgery and radiation therapy. Conventional approaches use an external tracker calibrated to the ultrasound transducer and CT system, but several calibration steps are required. Registration can also be performed by aligning image features between modalities, but differences in feature depiction make matching difficult and initial approximate alignment is often needed. Registration using fiducials is a simpler approach but is limited by the need to implant fiducials in the anatomical region of interest so they are visible to both ultrasound and CT. This paper investigates the feasibility of using fiducials near the skin surface, and whether such fiducials can be sufficiently localized in the very near field of a 3D ultrasound transducer without significantly degrading image quality. This approach can also be used as an initialization step for feature-based registration techniques.Materials and Methods: A stand-off pad containing fiducials (n > 3) was constructed using polyvinyl chloride and steel ball fiducials that are visible in both 3D ultrasound and CT images. Experiments on phantoms were performed to assess image quality and registration errors. Controlled variables included pad thickness and ultrasound imaging parameters. Initial tests were also conducted of a potential application in partial nephrectomy surgery.Results: Image quality was degraded by an average of 6-11-13% (elevational-axial-lateral) in resolution of point targets and 5% in lesion contrast. Average fiducial localization error was 1.34 mm (axial) to 2.38 mm (lateral and elevational); average fiducial registration error (FRE) was 0.46 mm (axial), 1.08 mm (lateral) and 0.90 mm (elevational); and average total registration error (TRE) was 1.84 mm (axial), 0.89 mm (lateral) and 3.31 mm (elevational). Clinical results showed a similar FRE to that in the phantom study, but with an average TRE of 14.04 mm (over three patients). Ultimate alignment of the organ boundaries was affected mainly by motion from respiration.Conclusions: The small loss of image quality from the fiducial stand-off pad and the minimal inconvenience of using the pad at the time of the CT scan may be a worthwhile trade-off for purposes of registration since the pad provides a registration accuracy of several millimeters while still allowing subsequent feature-based registration. Future research will focus on using the registration from the fiducial stand-off pad for deformable feature-based registration of 3D ultrasound to CT for tumor localization in renal surgery.

A method to map errors in the deformable registration of 4DCT images.

To present a new approach to the problem of estimating errors in deformable image registration (DIR) applied to sequential phases of a 4DCT data set. A set of displacement vector fields (DVFs) are made by registering a sequence of 4DCT phases. The DVFs are assumed to display anatomical movement, with the addition of errors due to the imaging and registration processes. The positions of physical landmarks in each CT phase are measured as ground truth for the physical movement in the DVF. Principal component analysis of the DVFs and the landmarks is used to identify and separate the eigenmodes of physical movement from the error eigenmodes. By subtracting the physical modes from the principal components of the DVFs, the registration errors are exposed and reconstructed as DIR error maps. The method is demonstrated via a simple numerical model of 4DCT DVFs that combines breathing movement with simulated maps of spatially correlated DIR errors. The principal components of the simulated DVFs were observed to share the basic properties of principal components for actual 4DCT data. The simulated error maps were accurately recovered by the estimation method. Deformable image registration errors can have complex spatial distributions. Consequently, point-by-point landmark validation can give unrepresentative results that do not accurately reflect the registration uncertainties away from the landmarks. The authors are developing a method for mapping the complete spatial distribution of DIR errors using only a small number of ground truth validation landmarks.

In Vivo Micro-Image Mosaicing

Recent advances in optical imaging have led to the development of miniature microscopes that can be brought to the patient for visualizing tissue structures in vivo. These devices have the potential to revolutionize health care by replacing tissue biopsy with in vivo pathology. One of the primary limitations of these microscopes, however, is that the constrained field of view can make image interpretation and navigation difficult. In this paper, we show that image mosaicing can be a powerful tool for widening the field of view and creating image maps of microanatomical structures. First, we present an efficient algorithm for pairwise image mosaicing that can be implemented in real time. Then, we address two of the main challenges associated with image mosaicing in medical applications: cumulative image registration errors and scene deformation. To deal with cumulative errors, we present a global alignment algorithm that draws upon techniques commonly used in probabilistic robotics. To accommodate scene deformation, we present a local alignment algorithm that incorporates deformable surface models into the mosaicing framework. These algorithms are demonstrated on image sequences acquired in vivo with various imaging devices including a hand-held dual-axes confocal microscope, a miniature two-photon microscope, and a commercially available confocal microendoscope.

SU‐GG‐J‐104: Inclusion of Effects of Image Registration Errors in Accumulated Dose Distributions

Purpose: To consider the effects of image‐registration error in dose accumulation across different geometry instances and to display the resultant errors in a meaningful and useful way. Method and Materials: 4DCT phases acquired of a lung cancer patient were non‐rigidly registered by a B‐spline interpolation method (www.plastimatch.org) to the first phase chosen as a reference geometry. Dose was calculated on each phase and warped back to the reference phase by linear interpolation. The error in the deformation values at each voxel were assumed to be independent of that of neighboring voxels or of adjacent phases. This allows an error instance to be simulated by randomly perturbing the deformation used in dose accumulation by a value sampled from a Gaussian distribution for each voxel. The dose was accumulated for each instance and thirty instances were simulated to sample the total error distribution. Three methods of assigning the standard deviation of the error distribution to each voxel were considered: (i) fixed value of 3mm; (ii) intensity‐matching method: the local value is scaled by a distance to agreement metric calculated by comparing the registered phase image with the reference image; and (iii) vector‐discrepancy method: the local value is scaled by evaluating the invertability of the deformation maps. The effects of the simulated error were visualized by a spread of the accumulated isodose contours. Results: The vector‐discrepancy method resulted in the representation of reduced errors in the posterior region of the target where the extra image detail provided by the ribs and vertebrae increased the accuracy of the registration. Differences between the intensity‐matching method and fixed‐error method were less noticeable. Conclusion: A method of including image registration error in dose accumulation has been developed. Further work is required to compare results to a gold standard on a number of image datasets.

MO-FF-A4-04: A Method to Construct Synthetic Maps of Spatially Correlated Deformable Image Registration Errors by Random Sampling of De-Correlated Error Modes

Purpose: To develop and test a method for constructing random synthetic maps of spatially correlated deformable image registration errors for estimating uncertainties in daily dose summation. Method and Materials: Two CTs were deformably registered 50 times using a variable region of interest (ROI) as the target of the registration. The displacement vector fields (DVFs) for anatomic motion included spatially correlated errors due to the variable ROI. Maps of the DVF error were created by subtracting the mean DVF from the individual DVFs for the volume shared by all ROIs. These DVF error maps were used as a training set to which principal components analysis was applied, producing spatially de-correlated modes of DVF error. These modes were sampled independently and used to reconstruct new synthetic maps of DVF error that reproduced the characteristics of the training set. Results: We applied three tests to show that a set of our sampled DVF error maps was statistically indistinguishable from a set of validation error maps: (1) the standard deviation of the sampled DVF errors was comparable to that of the validation set; (2) the eigenvalue spectra were the same for the sampled and validation sets; (3) the Kolmogorov-Smirnov test applied to the principal coefficient distributions for the two sets was consistent with their indistinguishability. Conclusion: We have developed a method to construct DVF error maps by sampling probability distributions of the spatially de-correlated error modes. We validated our procedure by demonstrating that maps of DVF error produced by our method were statistically indistinguishable from validation error maps. We propose to use this method to calculate the effect of DVF error on daily dose summation using deformable image registration.

Analysis of Feature Point Distributions for Fast Image Mosaicking Algorithms

In many algorithms the registration of image pairs is done by feature point matching. After the feature detection is performed, all extracted interest points are usually used for the registration process without further feature point distribution analysis. However, in the case of small and sparse sets of feature points of fixed size, suitable for real-time image mosaicking algorithms, a uniform spatial feature distribution across the image becomes relevant. Thus, in this paper we discuss and analyze algorithms which provide different spatial point distributions from a given set of SURF features. The evaluations show that a more uniform spatial distribution of the point matches results in lower image registration errors, and is thus more beneficial for fast image mosaicking algorithms.

A performance evaluation framework for association mining in spatial data.

The evaluation of the process of mining associations is an important and challenging problem in database systems and especially those that store critical data and are used for making critical decisions. Within the context of spatial databases we present an evaluation framework in which we use probability distributions to model spatial regions, and Bayesian networks to model the joint probability distribution and the structural relationships among spatial and non-spatial predicates. We demonstrate the applicability of the proposed framework by evaluating representatives from two well-known approaches that are used for learning associations, i.e., dependency analysis (using statistical tests of independence) and Bayesian methods. By controlling the parameters of the framework we provide extensive comparative results of the performance of the two approaches. We obtain measures of recovery of known associations as a function of the number of samples used, the strength, number and type of associations in the model, the number of spatial predicates associated with a particular non-spatial predicate, the prior probabilities of spatial predicates, the conditional probabilities of the non-spatial predicates, the image registration error, and the parameters that control the sensitivity of the methods. In addition to performance we investigate the processing efficiency of the two approaches.

Radiofrequency Ablation of Lung Tumors in Swine Assisted by a Navigation Device with Preprocedural Volumetric Planning

To develop an image guidance system that incorporates volumetric planning of spherical ablations and electromagnetic tracking of radiofrequency (RF) electrodes during insertion. Simulated tumors were created in three live swine by percutaneously injecting agar nodules into the lung. A treatment plan was devised for each tumor with optimization software to solve the planning problem. The desired output was the minimum number of overlapping ablation spheres necessary to ablate each tumor and the margin. The insertion plan was executed with use of the electromagnetic tracking system that guided the insertion of the probe into precomputed locations. After a 72-hour survival period, animals were killed and histopathologic sections of the tissue were examined for cell viability and burn pattern analysis. A planning algorithm to spherically cover the tumors and the margin was computed. Electromagnetic tracking allowed successful insertion of the instrument, and impedance roll-off was reached in all ablations. Depending on their size, the tumors and the tumor margins were successfully covered with two to four ablation spheres. The image registration error was 1.0 mm +/- 0.64. The overall error of probe insertion was 9.4 mm +/- 3.0 (N = 8). Analysis of histopathologic sections confirmed successful ablations of the tissue. Computer-assisted RF ablation planning and electromagnetically tracked probe insertion were successful in three swine, validating the feasibility of electromagnetic tracking-assisted tumor targeting. Image misregistration caused by respiratory motion and tissue deformation contributed to the overall error of probe insertion.

Sliding characteristic and material compressibility of human lung: Parametric study and verification

To find and verify the optimum sliding characteristics and material compressibility that provide the minimum error in deformable image registration of the lungs. A deformable image registration study has been conducted on a total of 16 lung cancer patients. Patient specific three dimensional finite element models have been developed to model left and right lungs, chest (body), and tumor based on 4D CT images. Contact surfaces have been applied to lung-chest cavity interfaces. Experimental test data are used to model nonlinear material properties of lungs. A parametric study is carried out on seven patients, 20 conditions for each, to investigate the sliding behavior and the tissue compressibility of lungs. Three values of coefficient of friction of 0, 0.1, and 0.2 are investigated to model lubrication and sliding restriction on the lung-chest cavity interface. The effect of material compressibility of lungs is studied using Poisson's ratios of 0.35, 0.4, 0.45, and 0.499. The model accuracy is examined by calculating the difference between the image-based displacement of bronchial bifurcation points identified in the lung images and the calculated corresponding model-based displacement. Furthermore, additional bifurcation points around the tumor and its center of mass are used to examine the effect of the mentioned parameters on the tumor localization. The frictionless contact model with 0.4 Poisson's ratio provides the smallest residual errors of 1.1 +/- 0.9, 1.5 +/- 1.3, and 2.1 +/- 1.6 mm in the LR, AP, and SI directions, respectively. Similarly, this optimum model provides the most accurate location of the tumor with residual errors of 1.0 +/- 0.6, 0.9 +/- 0.7, and 1.4 +/- 1.0 mm in all three directions. The accuracy of this model is verified on an additional nine patients with average errors of 0.8 +/- 0.7, 1.3 +/- 1.1, and 1.7 +/- 1.6 mm in the LR, AP, and SI directions, respectively. The optimum biomechanical model with the smallest registration error is when frictionless contact model and 0.4 Poisson's ratio are applied. The overall accuracies of all bifurcation points in all 16 patients including tumor points are 1.0 +/- 0.7, 1.2 +/- 1.0, and 1.7 +/- 1.4 mm in the LR, AP, and SI directions, respectively.

TH-D-213A-05: A Method to Estimate 4DCT Deformable Registration Errors Via Principal Components Analysis

Purpose: To extract continuous deformable image registration error maps from 4DCTs using a small set of ground truth landmarks. Method and Materials: Assuming that we have a set of displacement vector fields (DVFs) calculated via deformable registration from 4DCT breathing phases, and a small set of validation landmarks, we use principal components analysis (PCA) to separate the eigenmodes of breathing from the error eigenmodes. We then reconstruct the DVF error maps from their principal components. To test this method we made a 2D model of breathing motion in the thorax with a 16×16 pixel DVF to which we added simulated errors. We selected 20 pixels as ground truth landmarks and applied our PCA method to the simulated data to estimate the error maps. We applied the same algorithm to the Point-validated Pixel-base (POPI) 4DCT data set, which consists of a 4D CT in which clinicians have located 41 point landmarks in 10 reconstructed CT breathing phases. Results: In the numerical simulations our method successfully recovered the artificial DVF error map although the error amplitudes were underestimated by 10–30%. The 4DCT analysis showed PCA eigenvalue spectra that are consistent with the assumptions of our error estimation method and also indicated that the landmarks provided by POPI model are sufficiently representative to be used as ground truth for our analysis. Conclusion: Point-by-point landmark validation of deformable image registration results can give highly selective results that do not realistically reflect the true spatial distribution of registration errors. Our PCA based method allows a more realistic picture of image registration and 4DCT motion mapping errors. This research was supported in part by NIH grant P01CA116602.

TH-D-304A-07: Voxel-Based Kinetic Analysis Method Utilizing ROI Fragmentation

UPurpose: Kinetic analysis is important for accurate quantification of PET images. As it is typically done on the region of interest (ROI) level, it does not preserve spatial information of the tracer uptake. We developed a novel method for voxel‐based kinetic analysis on various spatial levels, which overcomes problem of high voxel noise level in dynamic PET images.Methods and materials: The proposed method starts with an ROI‐based kinetic analysis with the standard least‐squares method. Then a series of optimizations on sub‐regions is performed, where estimated parameters from the super‐region are used as initial guesses and a‐priori values for Bayesian parameter estimation procedure on sub‐regions. Procedure is repeated until sub‐regions consist of a single PET image volume element. The method was tested by comparing the model estimated parameters with the true parameters on a mathematical phantom. Several different a‐priori weighting schemes were tested on human cancer patients, dynamically imaged with FLT PET. Tracer kinetics was modeled with a two‐compartment four‐parameter kinetic model.Spatial variation of the kinetic parameters on parametric images was quantified. Results: Adding Bayesian part in the objective function greatly reduces spatial variation of kinetic parameters making images to appear smoother. On the other hand, the accuracy of parameter estimation is not compromised, as shown through phantom simulation studies. The reduction of spatial variation of kinetic parameter was found to be the most distinctive for k 3 parametric images, where variation was reduced approximately 6‐fold and the least evident for k i=k 1 k 3/(k 2+k 3) parametric images, where the reduction was approximately 2‐fold. Conclusion: The proposed method is unique because it does not incorporate population‐based prior knowledge, but develops prior knowledge by kinetic analysis on different spatial levels. It reduces spatial variation in parametric images, which reduces sensitivity to image registration errors, while quantitative accuracy is not decreased as with digital filtration.

A Stochastic Approach to Estimate the UncertaintyInvolved in B-Spline Image Registration

Uncertainties in image registration may be a significant source of errors in anatomy mapping as well as dose accumulation in radiotherapy. It is, therefore, essential to validate the accuracy of image registration. Here, we propose a method to detect areas where mono modal B-spline registration performs well and to distinguish those from areas of the same image, where the registration is likely to be less accurate. It is a stochastic approach to automatically estimate the uncertainty of the resulting displacement vector field. The coefficients resulting from the B-spline registration are subject to moderate and randomly performed variations. A quantity is proposed to characterize the local sensitivity of the similarity measure to these variations. We demonstrate the statistical dependence between the local image registration error and this quantity by calculating their mutual information. We show the significance of the statistical dependence with an approach based on random redistributions. The proposed method has the potential to divide an image into subregions which differ in the magnitude of their average registration error.

Highly robust ground moving target detection and relocation method for distributed satellites

The performance of ground moving target detection for distributed satellites will be affected significantly when there is an image registration error, clutter decorrelation and array error. In this paper, a new approach to moving target detection and relocation is proposed based on multi-channel and multi-pixel adaptive signal processing in an image domain. First, multichannel and multi-pixel joint data are equated to a simple array model. Given that there is an image registration error, the real steering vector of the moving target can be estimated through a space projection approach. The optimal beam forming approach is used to cancel clutter, and at the same time the cross-track velocity of the moving target can be determined by searching for the peak value of the cost function. The moving target can then be relocated on the SAR image. The simulation results indicate that this method has a good robustness to image registration error, clutter decorrelation and array error. The detection performance and the estimation accuracy are significantly improved.

An integrated analysis concept for errors in image registration

Image registration is an important ingredient in a wide variety of computer vision applications. Over the years countless algorithms emerged that allow for robust registration of image sequences. Unfortunately, high quality results still cannot be guaranteed in any case. Especially in interactive online systems that strongly rely on results of unsupervised registration algorithms, techniques for automatic quality analysis and failure compensation are indispensable. In this paper we present a new concept for an integrated and fully automatic detection and analysis of errors in registration. Based on a new metric for registration quality assessment, image differences are robustly detected. In addition, a hierarchical analysis scheme is proposed that allows distinguishing between various underlying error sources, all having different impacts on a registration result and requesting for individual compensation strategies.

MO-E-AUD B-06: A 4D Monte Carlo Dose Calculation Method for Clinical Applications

Purpose: The accumulated dose accuracy depends by both the image registration accuracy and the dose addition strategy. In this study, we introduce a Monte Carlo‐based approach for cumulative dose computation based on energy mapping between various datasets. Method and Materials: EGSnrc/DOSXYZnrc Monte Carlo code is modified such that the energy (rather than the dose) is mapped from a “source” dataset onto a “target” dataset. The dose is subsequently calculated as the ratio of the warped energy deposited and the warped mass. The latter is the sum of all source voxels mass weighted by the ratio of the number of particles from “source” to “target” and the total number of particles scored in the “source” voxel. A lookup table for the source‐to‐target distribution is created for each voxel. The cumulative dose calculation requires displacement vector fields (DVFs) between “source” and “target” images. We use, for exemplification, two different DVFs, one generated by using the ITK “demons”, and the other by using the visco‐fluid model registration method. Results: The algorithm is integrated with Pinnacle planning system and is demonstrated through a 4D treatment plan. The average difference between doses reconstructed using the two DVFs is 15.6% for mean lung dose, 13.6% for heart, and 2.1% for ITV. It appears that lung doses are affected the most by the DVFs used. Conclusion: The forward 4D MC method introduced here uses both mass and energy deposition sampling, is potentially more efficient, as it does not require tracking of the deformed boundary, and is expected to provide more accurate results than interpolation‐based dose accumulation approaches, especially for the lung dose calculation. However, it does not eliminate the bias introduced by image registration errors.

TH‐C‐AUD C‐05: Assessment of Intrafractional Motion for Spinal Radiosurgery Patients by Multiple Onboard Megavoltage CT Scans During Treatment

Purpose: To assess the intrafractional patient motion during single‐fraction spinal radiosurgery using multiple CT scans acquired with onboard megavoltage CT (MVCT) during treatment. Method and Materials: Nineteen patients underwent single‐fraction (12 – 24 Gy) spinal radiosurgery on a TomoTherapy HiArt radiotherapy unit with onboard MVCT. Because of the large fractional dose, the treatment was divided into 3 or more sub‐fractions. Patients were immobilized with BlueBAG™ BodyFIX® except for C‐spine patients who were immobilized with face‐and‐shoulder masks. To accurately align the patient, an initial MVCT was acquired after patient was setup to skin marks. Image registration between MVCT and planning CT was performed using an auto‐registration algorithm followed by manual fine tuning to calculate the couch shifts. Immediately after the alignment, a verification MVCT scan was acquired. The couch was further shifted according to verification CT before the first sub‐fraction was delivered. Subsequently, MVCT was reacquired and the patient realigned after each sub‐fraction. A total of 67 MVCT‐guided intrafrational alignments (excluding initial alignments) were evaluated for the 19 patients. Couch shifts were analyzed to obtain the information of patient intrafractional movements. Results: The mean ± standard deviation for the magnitude (and displacement which is expressed in parentheses) of the shift was 1.0±0.9 mm (0.16±1.31 mm) in the lateral direction, 1.2±1.1 mm (0.31±1.62 mm) in the anteroposterior direction, 1.6±1.2 mm (0.44±1.97 mm) in the superoinferior direction, and 2.5±1.4 for the resultant vector. The respective maximum shifts were 5.0 mm, 5.4 mm, 5.7 mm and 5.9 mm. Majority (73%) of the realignments required shifts less than 3.0 mm. Image resolution and registration errors may have contributed to the observed intrafractional motions. Conclusion: Patient intrafractional motion should be considered in treatment planning for spinal radiosurgery patients. More intensive intrafractional monitoring and better immobilization device are necessary to reduce intrafrational patient motion.

Non-rigid registration of hyperspectral imagery for analysis of agronomic scenes

Analysis of remote-sensing imagery usually entails the registration of images from multiple different wavelengths. Even though a staring instrument has the advantage of readily producing coherent spectral images, often these images still need some form of band-to-band registration to correct for instrument movement, pixel shift caused by vibration at different acquisition times or optical distortion introduced by difference in the optics. In this study, a method is reported to register hyperspectral images. The method consists of partitioning the pair of registering images (from different wavelengths) into multiple overlapping regions of interest (ROIs) and finding registration errors in each of these areas using the standard phase correlation (PC). The registration errors from the ROIs are then used to compute a geometric transformation, which is applied to the entire image to correct for non-rigid image registration errors that are mostly due to optical effects. This technique was tested on hyperspectral imagery acquired by a portable hyperspectral-tunable imaging system developed by the US Arid-Land Agricultural Research Center (USALARC) for ground and remote-sensing applications that include vegetative analysis for precision agriculture.

TU‐C‐M100F‐07: Detecting Dose Reconstruction Errors

Purpose In radiation therapy, delivered doses can be accumulated over fractions for adaptive treatment planning. However, the dose reconstruction fidelity can be compromised by image registration errors. The resultant dose discrepancy is hard to measure. This paper proposes a new method to assess the difference between the delivered dose and the warped dose. Method and Materials: The dose warping discrepancy is dominated by deformable image registration errors and source‐dose distributions. Registration errors can be specified within a finite element framework as an unbalanced energy δR, which is defined at element j by urn:x-wiley:00942405:media:mp1348:mp1348-math-0001 where E0 and di are Young's modulus and the displacement vector fields of the registration R. E0Φj is an assembly of all the element forces relating to the node i. Consequently the dose warping discrepancy at voxel k can be defined as the convolution of the dose divergence Div(D) and δR: urn:x-wiley:00942405:media:mp1348:mp1348-math-0002 The effectiveness of the dose‐discrepancy‐convolution (DDC) defined above is demonstrated through applying it to dose computed on ten prostate‐CT images. An IMRT treatment plan is developed on the planning image. In nine subsequent treatments, images are acquired to calculate the corresponding delivered doses. Their mean and standard‐deviation in Ci, a target contour automatically expanded from prostate delineated on the time‐of‐treatment image i, are compared with those of their warped doses measured on the planning target volume. The differences in their means and standard‐deviations are denoted by Eε and Eσ, respectively.Results δR, εD,R, Eε and Eσ are computed for the nine treatment fractions. Fraction one and eight have the largest warping discrepancies identified in all the four evaluation criterions. Conclusion Defined in terms of the deformable registration error, the voxel‐based DDC can be employed for the automatic evaluation of dose reconstruction in the whole dosing domain. Its measurement is consistent to the contour‐based dose warping evaluation performed in the planning target volume.

Investigation of Gamma Knife image registration errors resulting from misalignment between the patient and the imaging axis

The ability of Leksell GammaPlan to perform stereotactic space localizations with image sets where there is misalignment of the patient's head (stereotactic frame and fiducial apparatus) relative to the computed tomography (CT) scanner coordinate system was studied. Misalignment is sometimes necessary for patient comfort. Results equally apply to magnetic resonance imaging. Seven 0.5 mm diameter CT-visible spheres were rigidly mounted to a string tied tightly at each end to diagonally opposite posts attached to a Leksell stereotactic frame. A standard CT fiducial box was applied to the frame in the usual clinical manner. A baseline CT scan (1 mm slice thickness) was obtained with the fiducial box perfectly aligned with the scanner axis. After localization of the image set, the (x,y,z) coordinate of the center of each sphere was recorded. Repeat CT scans with varying fiducial box misalignments with the imaging axis were subsequently obtained. The mean difference between the base line and the respective coordinates in misaligned geometries was approximately 0.2 mm (sigma=0.2 mm), well within the accuracy of the image sets and the delivery of radiosurgery with the Gamma Knife.